Transformer system



April 12, 1960 u. A. MATsoN u 2,932,804'

TRANSFORMER SYSTEM /N VEN Tof? U. A MA 7`$ 0N y @ff/@wmf A 7' TOR/VE Y 5Sheets-Sheet 2 Filed Dec. 30, 1950 2 e y. 2 ,2 V 4 A N, N, 3 R C J J3,11 e CT o /NVENTOR U. A. MA 7'5 ON April l2, 1960 u. A. MATsoNTRANSFORMER SYSTEM 5 Sheets-Sheet S Filed Dec. 30, 1950 FIG. /2

"80 mman/cr f f w N E U 0 n F /NVENTOR U. A. MA TSON BV ggf/2M A TTORNEVApril l2, 1960 u. A. MA1-SON TRANSFORMER SYSTEM 5 Sheets-Sheet 4 FiledDec. 30, 1950 FREQUENCY f FREQUENCY f FREQUENCY f FREQUENCY f BECINVENTOR u. ,4. MM50/v BV www ATTORNEY April l2, 1960 Filed Dec. 50,1950 u. A. MATsoN 2,932,804

TRANSFORMER SYSTEM 5 Sheets-Sheet 5 www A 7' TORNE V Uno A. Matson,

2,932,804 -TRANSFORMER SYSTEM `Upper Montclair, NJ., assigner to BellTelephone Laboratories, Incorporated, New York, N.Y., a corporation'of-.New York Application December 30,.19`50,SexilNo. 203,656 $2 (Cl.43"'332f8) This invention relates to wa-ve transmission and moreparticularly to multiple 'transformer systems.

The object ofthe invention is to provide a wide-band transformersystemwhich has fa constant, non-reactive input image impedance `and a-voltage transformation which is constant or smoothly varying in bothamplitude and phase.

The transformer system or" the present `invention comprisesV alow-frequency `unit `and a highlfrequency unit, having adjoining oroverlapping transmission bands, connected between a common pair 'of'input Vterminals and a common pair of output terminals; .'Each unitcomprises a 'transformer and one :or :more associated networks which mayinclude either resistive or :reactive impedances, Aor combinationsthereof.I VIn one basic form the input sides of both units are connectedin series and the output sides are also connected in series. In anotherbasic form the output sides of the units are connected in series buttheir input sides areconnected in parallel. The associated networks may,for example, include resistances associated, respectively, with onewinding of each of thetransformers, an inductance shunting the primarywinding of one ofthe transformers, series combinations of resistance andcapacitance connected in shunt, respectively, with each winding of the`other transi former, and a series resistance separating theresistancecapacitance combinations. AAdditional impedance elements,either resistive or reactive, may be added for impedance correction orfor other purposes.

The values of the component impedance elements are so chosen that theinput image impedance of the transformer system is substantiallyconstantand non-reactive over the entire operating frequencyrange andthe voltage transformation ratio issubstantia'lly constant or variessmoothlyin Aboth magnitude and ``phase.vfi.n .import-ant feature of thesystem `is that the leakage Yinductance of the low-frequency transformeris made a part vof the basic structure, thus substantially Veliminatingtransmisunits adapted for use in the systems sion irregularitiesotherwise `caused thereby, especially near the junction ofthelow-.frequency andthe high-.frequency bands. The turns ratios of thetransformers may be selected to provide a gain-frequency characteristicwhich is substantially constannrises monotonically, or fallsmonotonically'. Corresponding to every gain` characteristic there arefour constant or smoothly varying phase shift-frequency characteristics,determined by the polling of the transformer windings.

The multiple transformer ,system in accordancewith the present inventionmay be'used to provide constant or smoothly varying `transmissionbetween any appropriate source and load..4 ift is particularly suitablefor use f between a vacuum jtube plate or grid of .high impedance f anda transmission line. jIt may also be used `to connectY two transmissionlines of different impedance,

The nature of the invention will be more fully understood from thefollowing detailed description and by reference to the'accompanyin'gdrawings, of which:

Fig. 1 is a schematic circuit of one basicrform of a multipletransformer system in accordance with the invention in which thelow-frequency unit and the highfrequency unit are connected in Aserieson both sides,

Figs. 2 and 3 are specific circuits of the general type shown in Fig. l;

Fig. 4 is a schematic circuit of another basic form in accordance withthe invention in which the units arerconnected in parallel on one sideand in series on the other;

Fig. 5 is a specific circuit of the general type shown in Fig. 4;

Fig. 6 is a schematic circuit of a ladder-type structure suitable foruseV as the associated networks N5, N6, N7 and N8 shown in block inFigs. l and 4;

Fig. 7 shows the circuit of the high-frequency `unit f1.2. of Fig. l orFig. 4 when the associated networks N7 and N8 are represented bygeneralized T-type structures;

Figs. 7A and 7B are `specific circuits `of high-frequency ,shown inFigs, l and 4, respectively;

Fig. 8 shows a circuit, used in analysis, equivalent to that of thelow-frequency unit 10 of Fig. l or Fig. 4 when the associated networksN5 and N6 are represented -by generalized T-type structures;

Figs. 8A and 8B are equivalent circuits representing low-frequency unitsadapted for use in the systems shown in Figs. 1 and 4, respectively;

Figs. 9, 10 and 1l show, respectively, typical flan, rising .and fallinggain-frequency characteristics obtain-l iferent poling arrangements ofthe windings of the trans- `formers T1 and T2;

IFigs. l5, 16 and `17 are vector diagrams showing'` the relationshipbetween the input and output voltages of the 'system of Fig. 1 or Fig. 4corresponding to the gain characteristics shown, respectively, Vin Figs.9, 10 and ll,

for one poling arrangement;

. Figs. 18, 19 and 2O are similar vector diagrams for another polingarrangement; v A

Fig. 2l is another speciic circuit of the general type shown in Fig. l,including additional impedance elements ffor high-frequencyequalizationgand Fig. l22 shows the gain-frequency characteristic .forthe transformer system of Fig. 2l.

Taking up the figures in greater detail, the jbasic form ofthe multipletransformer system shown in Fig. l comprises a four-terminallow-frequency unitl() andv a fourterminal high-frequency unit 11, eachshown enclosed in a brokenLline box, connected between a pair of inputterminals 1, 1' and a pair of output terminals 2, Z'. Any lsuitable wavesource, not shown, may be connected to the input terminals 1, 1 and anysiutable load impedance, notV shown, to the output terminals 2, 2. rIheunits 10 and 11 are connected in series on their input sides and also inseries on theirzoutput sides. The system may `be designed, ashereinafter explained, to have an input image impedance Z1 at terminals1l, 1' which is substantially a constant resistance and a voltage trans-'formation between terminals 1, `1' and terminals Z, 2

cross-over frequency, and unit 11 from, fx to f2. The

input voltage of the system at terminals 1, 1 is indicated Aas V1 andthe output voltage at terminals 2, 2' as V3.

The low-frequency unit lil comprises two tour-terminal whole or in partin the network N5 transformer T2 having a secondary winding 8--8 coupledby a low-frequency transformer T1 having a primary winding 5-5 and asecondary winding 6-6 with a turns ratio 1z1 between primary andsecondary. A iirst impedance branch comprising the series combination ofa resistance R1 and a capacitance C1 is connected in shunt between thenetwork N and the transformer T1, a second branch made up of aresistance R2 and an inductance L2 in series is interposed in seriesbetween the first branch and the transformer, and a third branchconsisting of Vthe series combination of a resistance R3 andacapacitance C2 shunts the secondary 6-6 of the transformer. Theresistance R2 includes the resistance of the primary and secondarywindings of the transformer T1 as referred to the primary side. Theinductance, L2 represents the leakage inductance between the transformerwindings as referred to the primary side. The component impedancebranches of the networks N5 and N5 are essentially resistive over abroad range of frequencies above and below the cross-over frequency fx,but for equalization purposes they may be allowed to become reactive inthe neighborhood of the cut-off networks N5 and N5 frequencies f1 andf2. The resistance corresponding to may be included in or the networkN5. The transformer T1 has its lower cut-off at the frequency f1 and isdesigned to transmit as wide a band as posthe core loss o f thetransformer T1 Y sible consistent with the magnitudes of the source andload impedances between which the system is to operate. Thehigh-frequency unit 11 comprises two four-terminalnetworks N1 and N8coupled by a high-frequency primary winding 7-7' and a with a turnsratio lz2 between primary and secondary. The primary winding 7-7 isshunted by an inductance L4 which preferably includes part'or all of themutual inductance between the windings of the transformer T2 as referredto the primary side. The networks N7 and N8 may include wholly or inpart the resistance of the windings of the transformer T2 and theresistance corresponding ,to the core loss. The component impedancebranches of the networks N2 and N5 arel essentially resistive over thefrequency range from f1 to f2 but may be made reactive near Vthe uppercut-o frequency f2' for equalization purposes. The transformer T2 isdesigned to transmit as wide a band as possible with f2 as the uppercut-off. The lower cutoff is in the neighborhood of fx.

Fig.' 6 shows a four-terminal network suitable for use as the networksN5, N5, N7 and N3. It is Va ladder-type structure' comprising seriesimpedance branches Z1, Z3, Z5 and ZN and interposed shunt impedancebranches Z2, Z1 and ZN 1. It will be understood, of course, that othertypes of equivalent networks may be substituted for the ladder type.Infits simplest form the network may reduce to a single series or shuntbranch. In some cases one or more of the networks may be omittedentirely.

Figs. 2 and 3 show simple forms of the transformer system of Fig. l. InFig. 2

R5, and the network N5 is` represented by the shunt resistance R11.V InFig. 3 'the networks N5 and N8 are omitted and the networks N5 and N7are represented by theshunt resistance R5 and R2, respectively.

Fig. 4 shows another basic form of the transformer system differing fromthat of Fig. 1 only in that the units 10 and 11 are vconnected inparallel, instead of in series, on their input sides. As explainedbelow, the system `may be designed to' have the same types of impedanceand transmission Ycharacteristics as those obtainable with the circuitshown in Fig. l.

A simple form of the system of Fig. Fig. 5, wherein the networks N5 andN5 the networks N5 and N7 are simply the series resistances R9 and R10,respectively.

The relationships between the values of the various component impedanceelements required 'to provide the 4 is shown in are omitted and thenetworks N5, and N, are A omitted, the network N5 is simply the shuntresistance be substantially true in a practical system over the er1--tire transmission band except in the neighborhood of the lower and uppercut-off frequencies f1 and f2. Therefore, the high-frequency unit 11 ofFigs. 1 and 4 is replaced by the equivalentcircuit shown in Fig. 7. Thenetwork N7 is a T structure comprising the series resistances R71 andR13 with an interposed shunt resistance R12 and the network N5 is asecond T structure made up of the series resistances R51 and R85 withthe resistance R82 connected in shunt therebetween. In'order tofacilitate identification, in

are enclosed in broken-line boxes.

f For use in the analysis of the system of Fig. l, the circuit of Fig. 7is converted to the equivalent circuit shown in Fig. 7A. Here, the turnsratio of vthe transformer T2 is aux, the value of the shunt inductancevis L2, the network N7 is now an L structure comprising a seriesresistance Rs followed by a shunt resistance Rx, and the network N8 isa` single series resistance R5.

In order to make the circuits shown in Figs. 7 and 7A equivalent, R5,R5, Rx, Lx and px have the following relationships with respect to thevalues given in Fig. 7:

For use in the analysislof the'system of Fig. 4, the circuit of Fig. 7Ais modified as shown in Fig. 7B. Here the transformer T2 has* a turnsratio qs, the shunt inductance a-value L11, and the network N1 is an Lfstructure comprising a shunt resistance Re followed by a seriesresistance R11. The following relationships are required in order tomakethe circuits of Figs. 7A and 7B equivalent: f` v resistance-capacitancebranches have approximately the same time constant, that is,

' C1R1=C3Rs (10) The theoretical value of the separating resistance R2is Figs. 7, 7A, 7B, 8, 8A and 8B the elements corresponding to thefour-terminal networks aaaasoa approximately equal 'to the sum of R1 andR3 when all three resistances are referred to the same side of thetransformer T1, that is,

The preferred actual value of this resistance is found byv subtractingfrom the value of R2, as determined by Equation 11, the resistance ofthe primary and secondary windings of the transformer T1 as referred tothe primary side. If the resistance of these windings is equal to R2, noadded resistance will be required.

For analysis, this low-frequency unit is replaced by the Vequivalentcircuit shown in Fig. 8. Here, the network N5 is a T structurecomprising the series resistance R51 and R53 with an interposed shuntresistance R52 and the network N6 is a second T structure constituted bythe series resistances R51 and R63 with the resistance R62 connected inshunt between them. It is also desirable that the portion of thelow-frequency unit 10 between the network N5 and N6 in Fig. 8 be of thesaine general configuration as the portion of the high-frequency unit 11between the works N1 and N8 in Fig. 7. In that each should comprise atransformer with a reactance shunting the primary winding. Thisreactance should be an inductance for unit 11 and a capacitance for unit10. Thus, Fig. 7 is of the proper' configuration for unit 11, the shuntinductance being L4. Fig. 8 shows Vthe desired configuration tance beingCX. In order to make the portion of the circuit of Fig. 8 between thenetworks N5 and N6 equivaient to the corresponding portion of thecircuitof Figs. 1 and 4, the resistances R1 and R3 are introduced, andthe following relationship must obtain:

For use in the analysis of the system of Fig. 1, the circuit of Fig. 8is modied as sworn in Fig. 8A. The turns ratio of the transformer T1 ischanged from b1 to py, the value of the shunt capacitance CX is changedto Cy, the network N5 is changed from a T structure to an`L structurecomprising a series resistance Rc followed by a shunt resistance Ry, andthe T structure of R R 2 @Form-Raggi 1) For` use in the analysis ofthesystem of Fig. 4, the circuit of Fig. 8A is modified as shown in`Fig. 8B. Here the transformer T1 has a turns ratio v, the shuntcapacitance a value Cv, andthe network N5 is an L structure for the unit10, the shunt capaci- 6 comprising a shunt resistance Rg followed by aseries resistance Rv. The' relationships required to make the circuitsof Figs. 8A and 8B equivalent are the following:

All of the required equivalent circuits have now been developed. In theanalysis which follows-it will be assurned that in the transformersystem shown in Fig. l the high-frequency unit 11 is equivalent to thecircuit of Fig. 7A and the low-frequency unit 10 is equivalent to thecircuit of Fig. 8A, and that in the system shown in Fig. 4 unit 11 isequivalent to the circuit of Fig. 7B and unit 10 is equivalent to thecircuit of Fig. 8B.

In order to insure thatV the input image impedance ZI for both of thesystems will be constant and non-reac-` tive throughout the frequencyrange from f1 to f2, it is necessary to establish two additionalrelationships, besides those already given. These are, for Fig. rl,

` Expressions giving the output voltage V2 at` terminals v2,2 of thesystem in terms of the input voltage V1 at terminals 1, 1 will now bepresented for the circuits shown in Figs..1 and 4. Four diiferent casesare to be distinguished, depending upon the poling arrangement employedfor the windings of the transformers T1 and T2.

For conditionY which gives minimum phase shift, the windings are sopoled that a series aiding connection for transformer T1 results ifterminals 5 of the primary winding is connected to terminal 6 of thesecondary winding, and also a series aiding connection for transformerT2 Vresults if terminal 7' is connected to terminal 8. In this case, forFig. 1,

and w is `the angular frequency at any frequency f. In Equations 29 and30, plus signs are used where alternatives are given. r

In Equation 29, the term in which py appears is the output voltage ofthe low-frequency unit Ain Fig. 1, and the ,term including qtx'is theoutput voltage of the highfrequency unit 11. In Equation 30, the termincluding p v represents the output voltage of unit 10 in Fig. 4, andthe term in which 4: appears is the output voltage of unit 11. t

For condition II the windings are so poled that, with the terminalsconnected as indicated under condition I, a series opposing connectionwould be obtained in each of the transformers. Under these circumstancesthe output voltage for Fig. 1 is given by Equation 29 and that for Fig.4 by Equation 30, using minus signs where alternatives are given. i l

For condition III the windings are so poled that, with similarconnections of the terminals, a series aiding connection would resultfor T1 but a series opposing connection for T2. For this case the outputvoltages for Figs. 1 and 4 may be foundfrom Equations 29 and 30,respectively, using plus signs for the first alternative and minus forlthe second.

For condition IV the windings are so poled that, with similarconnections of the terminals, a series opposing connection would beobtained for T1 'out a series aiding A connection for T2. Here, theoutput voltage for Fig. l is given by Equation 29 and that for Fig. 4 byEquation 30, using minus signs for the first alternative and plus forthe second.

The various types of transmission and vphase shift characteristicsobtainable with the transformer systems shown in Figs. 1 and 4 will nowbe considered. Since the two circuits are potentially equivalent exceptfor the flat loss, any type of characteristic given by one may,'byproper design, be duplicated in the other. There are three general typesofy gain-frequency characteristics, at, rising, or ,i

falling, as shown in Figs. 9, 10, and 11, Vdepending upon the choicerofthe turns ratios for the transformers','Ifiv and T2. For each gaincharacteristic' there are four types of phase shift-frequencycharacteristics, as shown in Figs.

12, 13, and 14, corresponding to the polingof the transformer windings.For Fig. 1 if px and rpy, shown' in Figs. 7A and 8A, are equal, or forFig. 4 if ai and ipv, shown in Figs. 7B and 8B, are equal, the gain willbe constant over the frequency range between f1 and f2, as shown bycurve 12 in Fig. 9,

where gain in decibels is plotted against the frequency f. The amount ofgain depends upon themagnitudeioflthc equal turns ratio. For aproperchoice of this magnitude the gain can be made positive, as shownbycurve 12, zero or negative. When the gain is fiat, the phasecharacteristic may take any one of the forms shown by the curves I, II,III and IV in-Fig. 12, where the designations correspond with the fourpoling conditions described above. In curve I the phase shift is zeroand in curve II it is --180 degrees throughout the band, in curve III itfalls smoothly from zero to l80 degrees, and in curve IV rises smoothlyfrom 180 degrees to zero.

Fig. l0 shows the type of gain characteristic obtainable if qx isgreater than py for Fig. 1 or u is greater than pv for Fig. 4. ".,Thegainv rises monotonically with frequency and, depending upon themagnitudes ofthe turns ratios chosen, may bew entirely above,'1:ross, orbe entirely below the axis asi show nby the typical curves 13, 14 and15, respectively. AThe corresponding phase characteristics for polingconditions I, II, III and IV are shown by the similarly designatedcurves in Fig. 13.

l lrninals 2, 2.

. If px is less than 1 for-.Fig-.V 1 or pu is less than pv v for Fig. 4,the gain characteristic falls monotonically with frequency as shown bythe typical curves in Fig. l1. Depending upon thermagnitudes of theturns ratios 'selected, the gam maybe all positive, go from positive tonegative, or be all negative, as shown, respectively, by

the curves 16, .17 andIS. .The phase characteristics associated withpoling 'conditions I, II, III and are shown by the correspondinglydesignated curves in-Fig.14. -1

If desired, a vector diagram may be used to find graphically at anyfrequency f the relationship between the output voltage V2 and the inputvoltage V1, from Ywhich the gain characteristic of the transformersystem may be determined, and also the phaseangle between thesevoltages, which correspondsto the phase shift. Typical vector diagramsfor ideal circuits of the types shown in Figs. 1 and 4 are presented inFigs. 15 through 20. Figs. 15, 16 and 17 correspond to the 'at, risingand fallinggain characteristics shown in Figs. 9, 10 and V11,respectively, for poling condition I with minimum phase characteristicsshown by curves I inFigs. l2, 13 and 14, respectively. The diagrams inFigs. 18, 19 and 20 also relate tothe gain characteristics shown inFigs. 9, 10 and 11, respectively, but are for poling condition III withphase characteristics shown by curves III in Figs. 12, 1 3 and 14,respectively. Of course, similar sets of vector diagrams may beconstructed for poling conditions II and IV.

In each of the diagrams the input voltage V1 of the system at terminals1, 1' is represented by a vector, not shown, extending from the origin Ohorizontally to the right a distance corresponding to the magnitude ofV1. 'Ihe vector OA represents the output voltage of the highfrequencyunit 11 at a selected frequency f within the band ofthe system, thevector OD, which always makes a right angle with OA, represents theoutput voltage of ,the low-frequency unit 10, and OE is the resultantvector representing the output voltage V2 of the system at ter- At thelower cut-off frequency ,f1 the terminus of the vector OA coincides withtheorigin O, and as the frequency increases to f2 the terminus traversesthe semicircular path OAB to the point B. The terminus of the vector ODstarts at the Vpoint C for the frequency f1 and, as the frequencyincreases to f2, follows the semicircular path CDO to the origin O. Atthe frequency f1 the terminus of the resultant-vector OE is at 'thepoint C and, as the frequency increases, traces the semicircular pathCEB to the point B.

In the diagram ofFig. 15,' corresponding to constant gain and polingcondition I, it will be noted that the path of the terminus of theresultant vector 4GF. shrinks to -a point. That is, the points B, C andE coincide. This means that ideally the phase shift is zero through-`outthe band, as shown by curve I in Fig. l2. In Fig. 16, whichcorresponds to rising gain and poling condition I, the resultant vectorOE always increases in length with frequency and makes a positive anglewith the horizontal which rst increases and then ldecreases Ainmagnitude. Therefore the gain characteristic, shown in Fig. 10, riseswith frequency andthe phase characteristic, given by curve I in Fig. 13,has a positivehump. In Fig. 17, however, the vector OE decreasescontinuously with frequency and makes at rst an increasing and then adecreasing negative angle with the horizontal. This means that thecorresponding gain characteristic, given in Fig. 11, falls withfrequency shown by curve I in Fig. 14, has a negative hump. In Fig. 18,which corresponds tol hat gain and poling condition III, the vector OEhas the same length at al1 fre quencies but makes a negative angle withthe horizontal which starts at zero and increasesV to degrees. The phasecharacteristic, given by curve III in Fi'g. 12, therefore fallscontinuously from zero to -180 degrees. From this partial -analysis ofthe vector diagrams given i n Figs. 15 to 20 it will be apparent thatthey are very useful tools for determining, at least'qualitatively, boththe gain and the phase characteristics of the transformer systems,without resorting to formulas such as 29 and L"5() which give explicitythe output voltage V2 in terms of the input voltage V1.

For simpler structures the required relationships between the componentelements given above for the generalized transformer systems of the-typeshown in Figs.; 1 land`4 take a simpler form. lFor' example, theonlynep@- andthe phase characteristic,

ance LM represents sary relationships applying to the circuit of Fig.. 2are those given by Equations 10, l1 and the following:

. andthe choice of sign in the two placeswhere alternatives are given.depends upon the poling condition of the transformer windings, asdescribed above. For condition I both signs are plus, for condition IIboth are minus, for condition III the irst is plus and the second minus,and for condition IV the first is minus and the second plus.

Fig. 2l shows schematically the circuit of a multiple transformer systemof the Fig. l type designed to cover a frequency range extendingapproximately from 10 cycies to 8.5 megacycles per second, when workingout of a resistive impedance and into a Vacuum tube of high im pedanceconnected to the output terminals 2, 2. The voltage gain, expressed indecibels, between input and output is shown in Fig. 22 plotted againstthe frequency f in kilocycles, using a logarithmic scale. It will benoted that the characteristic issubstantially flat over the entire rangefrom f1 to f2, with no appreciable irregularities in the region of thecross-over frequency fx between the llow-frequency band of unit 10 andlthe high-frequency band of unit 11. 7

ln Fig. 2l the elements C3, L2, R1, R2, R3, T1 and T2 correspond tothose similarly designated in Fig. l. The resistance R5 represents thenetwork N5 of Fig. 1, the resistances R71 yand R72 represent the networkN7 and the resistances Ran, Rab, and R8c represent the network N8.Network N6 is omitted. The required relationships between the values ofthese elements aregiven in the design formulas already presented. Theshunt inductthe inherent mutual inductance of transformer T1 as referredto the primary side. This mutual inductance causes the voltage gain tofall o' below the'fi'eqnency f7, as shown in Fig. 22. The capacitancesC4, C5, C6, C7 and Ca and the inductances L5, La and L7 are added toprovide gain equalization in the neighborhood of the upper cut-oiffrequency f2. The values of these reactances are selected or adjusted togive the hattest possible band. The capacitance Cl' has approximatelythe value given by the equation The value of C1 may be obtained fromEquation 10.

What is claimed is:

l. A multiple transformer system comprising two trans- Lif) a fthresistance and a first inductance effectively in series with one of saidresistance-capacitance combinations and a winding of said Ersttransformer, and a second inductance shunting a winding of said secondtransformer, said resistance-capacitance combinations havingapproximately the same time constant, said fifth resistance beingapproximately equal to the sum of said third and fourth resistances whenall three are referred to the same side of said rst transformer, and theratio of said first inductance to the sum of saidvcapacitances, when allthree are referred to the same side of said first transformer, beingapproximately equal to the product of said third and fourth resistanceswhen both are referred to said same side of said first transformer.

2. A system in accordance with claim l in which said transformers areconnected in series on 'both sides.

3. A system in accordance with claim 2 in which said rst resistance isconnected in shunt with a winding'v of said first transformer and saidsecond resistance is co nected in shunt with a winding of said secondtransformer.

4. A system in accordance with claim 2 in which said first and secondresistances are connected in shunt, respectively, with the secondarywindings of said transformers.

5. A system in accordance with claim 2 in which said rst and secondresistances are connected in shunt, respectively, with the primarywindings of said transformers.

6. A system in accordance with claim'l in which said transformersareconnected in parallel on one side and in series on the other side.

7. A system in accordance with claim 6 in which said first resistance isconnected in series with a winding of said rst transformer and saidsecond resistance is connected in series with a winding of said secondtransformer.

8. A system in accordance with claim 6 in which said transformers areconnected in parallel 'on their input sides.

9. Asystem in accordance with claim 8 in which said first and secondresistances `are connected in series, re spectively, 'with the primarywindings of said transformers. 7 -v 10. A system in accordance withclaim l in which said fifth resistance is on the input side of saidfirst transformer. l i v l1. A system in accordance with claim l linwhich said fifth resistance includes the effective resistance of thewindings of said rst transformer. f

12. A system in accordance with claim l which has an input imageimpedance which is substantially constant and non-reactive over thetransmission band of the system.

13. A system in accordance with claim l which includes additionalimpedance elements for impedance corat one end to a windingof the rst ofsaid transformers, a i

second resistance connected at one end to a Winding of the second ofsaid transformers, the other ends of said resistances `being connectedtogether, the series combination of a third resistance and a firstcapacitance connected to the terminals of one winding of said lirsttransformer, the series combination of a fourth resistance and a secondcapacitance connected to the'terminals of the other winding of saidfirst transformer, the series combination of rection within thetransmission band. f

14. A multiple transformer system comprising two transformers havingprimary windings connected in series, secondary windings connected inseries and adjoining transmission bandsa resistance R8 shunting thesecondary of one of said transformers, an inductance L4 shunting theprimary of saidone transformer, a resistance R6 shunting the secondaryof the other of said transformers, the seriescombination of a resistanceR1 and a capacitance C1 shunting the primary of said other transformer,a resistance R2 effectively in series with the primary of said othertransformer, and the series combination of a resistance R3 and acapacitance C3 shunting the secondary of said other transformer, thecomponent elements of said system being proportioned with respect to theinherent leakage inductance L2 between the windings of said othertransformer to provide a substantially smooth transmissioncharacteristic for the system over a frequency range extending from thelower end of one of said bands to the upper end of the other of saidbands and an input image impedance which is substantially con- 11 stantand non-reactive over said'frequency range, and said elements havingapproximately the following relationships: v

C1R1= C3133 R2=Ri+Rsx2 L2 naa Cri C312 1511l v and where o1 is the turnsratio between the primary and the secondary windings of said onetransformer and p2 is the turns ratiol between the primary and thesecondarywindings of said other transformer. l

15. A system in accordance with claim 14 in which the resistance R2includes the effective resistance of the windings of said rsttransformer.

16. A system in accordance with claim 14 which includes additionalimpedance elements for impedance correction within the transmissionband.

17. A system in accordance with claim 14 in which said vresistance R2 iseffectively located between the primary of said other transformer andsaid combination of R1 C1. i

18. A system in accordance with claim 14 in which said transformers haveequal turns ratios.

19. A system'in accordance with claim 14 in which the windings of saidvtransformers are poled for minimum phase shift throughout said bands.

20. A system in accordance with claim 19 in which said transformers haveequal turns ratios.

21. A system in accordance with claim 1 in which the ratio of saidsecond inductance, as referred to the input side of said secondtransformer, to the sum of said capacitances, as referred to the inputside of said iirst transformer, is approximately equal to the square ofsaid second resistance, as referredto theinput side of said secondtransformer. 1

22. A system in accordance with claim 1 in which the ratio of saidsecond inductance, as referred to the input side of said secondtransformer, to the sum of said capacitances, as referred to the inputside of said first transformer, is approximately equal to the square ofthe sum Aof said first and fourth resistances, as referred toV the inputside of said first transformer.

23. A system in accordance with claim 1 in which the ratio of saidsecond inductance, as referred to .the input side of said secondtransformer, to the sum of said capacitances, as referred to the inputside of'said first transformer, is approximately equal to the square ofsaid second resistance, as referred to the input side of said secondtransformer, Vand is also approximately equal to the square of the sumof said first and fourth resistances, as referred to the input side ofsaid first transformer.

24. A system in accordance with claim 1 in which said first inductanceincludes the leakage inductance of said first transformer. Y

25. A System in accordance with claim 1 in which the windings of saidtransformers are poled for minimum phase shift throughout said bands.

26. A system in accordance with claim 25 in which the turns ratios ofsaid transformers are chosen to provide a substantially fiat gaincharacteristic throughout said bands.

27. A system in accordance with claim 1 in which the windings of saidtransformers are poled for maximum phase shift throughout said hands. v

28. A system in accordance with claim 1 in which the windings of saidtransformers are poled for a falling phase shift throughout said bands.

29. A system in accordance with claim 1 in which the' windings of saidtransformers are poled for arising phase shift throughout said bands.

30. A system in accordance with claim 1 in which the turns ratios ofsaid transformers are chosen .to provide a substantially fiat gaincharacteristic throughout said bands. Y

31. A system in accordance with claim 1' in which the turns ratios ofsaid transformers are chosen to provide a rising gain characteristicthroughout said bands.

32. A `system in accordance with claim 1 in which the turns ratios ofsaid transformers are chosen to provide a falling gain characteristicthroughout said bands.

References Cited in the tile of this patent UNTTED STATES PATENTS2,024,900 Wiener et al. Dec. 17, 1935 2,067,444 -Gewertz Jan. 12, 19372,301,245 Bode Nov. 10, 1942

